The present invention relates to an optical imaging system used in an image transmission portion of an optical device, for example, a facsimile device, a copier, a printer, a scanner, or the like. More particularly, the present invention relates to an optical imaging system including a rod lens array, in which a plurality of rod lenses are arranged in an array.
In an optical device, for example, a facsimile device, a copier, a printer, a scanner, or the like, to read out information on a manuscript plane by converting the information into an electrical signal, various kinds of scanning devices are used. One form of the scanning device is a contact type device. This contact type scanning device is formed by incorporating various parts including a lightening system, a rod lens array that is a one-to-one imaging device, a sensor, a cover glass (a transparent substrate), and the like, into one frame. In general, a manuscript is brought into contact with the surface of the cover glass and illuminated by the lighting system. The illuminated manuscript is imaged on the censor by the rod lens array and converted into an electric signal. Herein, the rod lens array is a one-to-one optical imaging system in which a plurality of rod lenses having a refractive index distribution in a radial direction are arranged in one row or two rows (see FIG. 2).
An example of a lens material used for a rod lens array includes glass, synthetic resin, or the like. A glass lens having a refractive index distribution is produced, for example, by an ion exchange method.
A single rod lens forms a one-to-one image within the range of a circle having a radius X0 (field of view). The quantity of light is at the maximum on the optical axis and decreases with greater distance from the optical axis. Therefore, the distribution of the quantity of light in the longitudinal direction of a rod lens array has irregularity with the period corresponding to the distance between lenses. The magnitude of the irregularity of the quantity of light is defined as: 100 {(maximum quantity of light)-(minimum quantity of light)} /(minimum quantity of light) %, and determined by the overlapping degree m expressed by the following equation (Eq. 3):
m=X0/2R xe2x80x83xe2x80x83(Eq. 3) 
wherein 2 R denotes the distance between the optical axes of neighboring rod lenses.
FIG. 15 shows a relationship between the overlapping degree m and the irregularity of the quantity of light, which are calculated by the below mentioned equation of the distribution of the quantity of light (Eq. 9), in a rod lens array in which a plurality of rod lenses are arranged in two rows. FIG. 15 shows the case of so-called xe2x80x9clinear scanning methodxe2x80x9d using a very narrow range of light on the central axis of the image plane (see FIG. 2). As shown in FIG. 15, the irregularity of the quantity of light tends to decrease as the overlapping degree m is increased. However, the irregularity does not decrease monotonically. For example, at the points of m=0.91, 1.13, 1.37, 1.61, 1.85 . . . , the irregularity of the quantity of light takes on local minimum values. Since the irregularity of the quantity of light on the sensor should be as small as possible, when it is necessary particularly to minimize the irregularity of the quantity of light, the rod lens array is designed so that the overlapping degree m is approximate to the above-mentioned values. However, the irregularity of the quantity of light shown in FIG. 15 is the value when the sensor is arranged exactly on the central axis of the image plane. Therefore, in actual mass-produced scanning devices, it is inevitable that a dislocation between the sensor and the optical axis of an entire rod lens array occurs to some extent due to errors in dimensions of components or errors in assembling components. The dislocation of the sensor is defined as xcex94X in FIG. 9. Accordingly, it is suggested that the device is designed so that the overlapping degree m is shifted somewhat from the above-mentioned local minimum values, in order to allow the irregularity of the quantity of light to fall within the range of not more than a certain level even if the dislocation of the sensor occurs to some extent (JP 11(1999)-14803A, JP11(1999)-64605A).
In general, even in the case of a rod lens array using rod lenses having the same optical characteristics, as the overlapping degree m becomes smaller, the brightness of the image plane is enhanced, and the resolution power is increased. FIG. 16 shows the relationship between the overlapping degree m and average brightness (in the case of a linear scanning) in a rod lens array in which a plurality of the same rod lenses are arranged in one row and in two rows. In FIG. 16, the brightness of the rod lens array is defined to be 100 when the overlapping degree m is 1.50 and the rod lenses are arranged in two rows in the rod lens array.
However, as the overlapping degree m is smaller, the irregularity of the quantity of light is increased. Thus, in a practical rod lens array, the overlapping degree m is 1.3 or more in the case of a rod lens array in which the rod lenses are arranged in two rows. For example, the lower limit of the overlapping degree m is set to be 1.36 in the rod lens array in which the rod lenses are arranged in two rows by Nippon Sheet Glass Co., Ltd. According to a disclosure of JP11(1999)-14803A, the desirable overlapping degree m is set to be in the range of 1.46xe2x89xa6mxe2x89xa61.64.
Recently, to provide high speed for a facsimile device, a scanner, or the like, a brighter rod lens array has been demanded.
It is an object of the present invention to provide a high performance optical imaging system by minimizing the overlapping degree m, increasing the quantity of light of the rod lens array and improving the resolving power while taking into account the irregularity of the quantity of light when a dislocation between a sensor and an optical axis of an entire rod lens array occurs.
In order to achieve the above-mentioned object, the configuration of the optical imaging system for focusing light from a manuscript plane onto an image plane according to the present invention includes a rod lens array having a plurality of rod lenses with a refractive index distribution in a radial direction that are arranged in two rows so that their optical axes are in parallel to each other. An overlapping degree m expressed by the following equation (Eq. 4) is in a range of 0.91xe2x89xa6mxe2x89xa61.01;
m=X0/2R xe2x80x83xe2x80x83(Eq. 4) 
wherein 2 R denotes a distance between the optical axes of neighboring rod lenses and X0 denotes an image radius that the rod lenses project onto the image plane.
According to such a configuration of the optical imaging system, it is possible to obtain a high performance optical imaging system in which a quantity of light is increased and the resolution power is improved.
Furthermore, in the configuration of the optical imaging system of the present invention, it is preferable that the overlapping degree m is in the range of 0.93xe2x89xa6mxe2x89xa60.97.
Furthermore, in the configuration of the optical imaging system of the present invention, it is preferable that R is in the range of 0.05mmxe2x89xa6Rxe2x89xa60.60 mm. When R is less than 0.05 mm, production of the rod lens array becomes difficult from the practical viewpoint (for example, handling becomes extremely difficult). When R is more than 0.60 mm, the entire rod lens array becomes large, it is difficult to downsize the entire optical imaging system.
Furthermore, in the configuration of the optical imaging system of the present invention, it is preferable that a radius r0 of a portion functioning as a lens of the rod lenses is in the range of 0.50 Rxe2x89xa6r0xe2x89xa61.0 R. When r0 is less than 0.50 R, the brightness of the image is remarkably reduced. Therefore, it is needless to say that the maximum r0 is equal to R.
Furthermore, in the configuration of the optical imaging system of the present invention, it is preferable that a shading mask having an approximately rectangular shaped opening portion opening along the longitudinal direction of the rod lens array is arranged on at least one side of the rod lens array. According to such a preferable configuration, it is possible to reduce the irregularity of the quantity of light. Furthermore, in this case, it is preferable that the opening portion of the shading mask is symmetric to the central axis in the longitudinal direction of the lens surface of the rod lens array. Furthermore, it is preferable that a half width W of the opening portion of the shading mask is in the range of ({fraction (3/2)})R+0.1 r0xe2x89xa6Wxe2x89xa6({fraction (3/2)}) R+0.6 r0, wherein r0 denotes a radius of a portion functioning as a lens of the rod lenses. When the half width W of the opening portion of the shading mask is less than ({fraction (3/2)}) R+0.1 r0, the quantity of light is much lowered. When the half width W is more than ({fraction (3/2)}) R+0.6 r0, no significant improvement of the irregularity of the quantity of light is realized.
Furthermore, in the configuration of the optical imaging system of the present invention, it is preferable that the refractive index distribution of the rod lenses is expressed by the following equation (Eq. 5);
n(r)2=n02xe2x80xa2{1xe2x88x92(gxe2x80xa2r)2+h4xe2x80xa2(gxe2x80xa2r)4+h6xe2x80xa2(gxe2x80xa2r)6+h8xe2x80xa2(gxe2x80xa2r)8+. . . }xe2x80x83xe2x80x83(Eq. 5) 
wherein r denotes a radial distance from an optical axis of the rod lenses, n0 denotes a refractive index at the optical axis of the rod lenses, and g, h4, h6 and h8 denote coefficients of the refractive index distribution. Furthermore, in this case, it is preferable that the refractive index n0 at the optical axis of the rod lenses is in the range of 1.4xe2x89xa6n0xe2x89xa61.8. Furthermore, in this case, it is preferable that a product n0xe2x80xa2gxe2x80xa2r0 is in the range of 0.05xe2x89xa6n0xe2x80xa2gxe2x80xa2r0xe2x89xa60.50, wherein r0 denotes a radius of a portion functioning as a lens of the rod lenses. According to such a preferable configuration, it is easy to produce rod lenses. Furthermore, in this case, it is preferable that Z0/P is in the range of 0.5 less than Z0/ P less than 1.0, wherein Z0 denotes a length of the rod lens and P=2xcfx80/g denotes a one-pitch length of the rod lenses. According to such a preferable configuration, an erected image can be obtained.
Furthermore, in the configuration of the optical imaging system of the present invention, it is preferable that a parallel plane transparent substrate is arranged so that the manuscript plane is positioned at a front focal position of the rod lens array. According to such a preferable configuration, the manuscript plane can be set at the front focal position just by pressing the manuscript to the surface of the transparent substrate. In this case, it is preferable that the parallel plane transparent substrate is in contact with the lens surface of the rod lens array. This easily can be realized by adjusting the thickness of the transparent substrate. According to such a preferable configuration, the adjustment of the distance between the rod lens array and the front focal position can be simplified, which makes the assembly of the optical imaging system cheaper.